Question: All of the 4th grade teachers and students from Loyola went on a field trip to an archaeology museum. Tickets were $$8.00$ each for teachers and $$2.50$ each for students, and the group paid $$47.00$ in total. A few weeks later, the same group visited a natural history museum where the tickets cost $$32.00$ each for teachers and $$10.50$ each for students, and the group paid $$191.00$ in total. Find the number of teachers and students on the field trips.
Answer: Let $x$ equal the number of teachers and $y$ equal the number of students. The system of equations is: ${8x+2.5y = 47}$ ${32x+10.5y = 191}$ Solve for $x$ and $y$ using elimination. Multiply the top equation by $-4$ ${-32x-10y = -188}$ ${32x+10.5y = 191}$ Add the top and bottom equations together. $ 0.5y = 3 $ $ y = \dfrac{3}{0.5}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $ {8x+2.5y = 47}$ to find $x$ ${8x + 2.5}{(6)}{= 47}$ $8x+15 = 47$ $8x = 32$ $x = \dfrac{32}{8}$ ${x = 4}$ You can also plug ${y = 6}$ into $ {32x+10.5y = 191}$ and get the same answer for $x$ ${32x + 10.5}{(6)}{= 191}$ ${x = 4}$ There were $4$ teachers and $6$ students on the field trips.